Find the value of x on this right triangle when a=20 b=5x-10 and c=2x(Square root of 5)

A. x = 15
B. x = 10
C. x = 12
D. x = 16

A wheel 5.00 ft in diameter rolls up a 15.0° incline. How far above the base of the incline is the top of
the wheel after the wheel has completed one revolution?
A. 13.1 ft
B. 8.13 ft
C. 9.07 ft
D. 4.07 ft

Solar panels are used to convert energy from the sun into electricity. To get the best result, the panel
has to be perpendicular to the sun's rays; in other words, angle è has to be a right angle. What should the height, h, be if è is a right angle, a solar panel is 12 ft long, and the sun's angle of elevation is 38°?

A. 9.4 ft
B. 9.5 ft
C. 15.4 ft
D. 7.4 ft

Which of the following pairs of angles are coterminal?
A. 100° and 620°
B. 25° and –25°
C. 390° and 750°
D. 30° and 60°

?

D
B
C

To find the value of x in a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In the first question:
We have side a = 20, side b = 5x - 10, and side c = 2x(sqrt(5)).
Using the Pythagorean theorem: a^2 + b^2 = c^2.
Substituting the values: (20)^2 + (5x - 10)^2 = (2x(sqrt(5)))^2.
Simplifying the equation and solving for x, we get:
400 + 25x^2 - 100x + 100 = 20x^2(5).
Combining like terms and simplifying further, we get:
25x^2 - 100x + 100 - 400 = 0.
Simplifying further, we get:
25x^2 - 100x - 300 = 0.
To find the value of x, we can factorize the equation or use the quadratic formula.

For the second question:
To find how far above the base of the incline the top of the wheel is, after the wheel has completed one revolution, we need to find the vertical distance it has traveled. This distance can be found by calculating the height of the arc traveled by the wheel.

The height of the arc traveled by the wheel can be found using the formula:
Height = Radius * (1 - cosθ),
where θ is the angle of the incline (15°).

In the third question:
We are given the length of the solar panel (12 ft), the sun's angle of elevation (38°), and we need to find the height (h) to make angle è a right angle.

In the fourth question:
Coterminal angles are angles that share the same initial and terminal sides when drawn in standard position. They differ in their number of complete rotations. Two angles are coterminal if their difference is a multiple of 360°.

To determine which pairs of angles are coterminal, we need to find the difference between the angles and check if it is divisible by 360°.

Based on the explanations provided, the user can now determine the correct answers to the questions by either solving the equations or using the formulas mentioned.